Enter what you measured and the known accepted value — get the percent error and the signed absolute error side by side.
Percent error is |experimental − true| ÷ true × 100. With the values this page opens with — a measurement of 48 against a true value of 50 — the absolute error is −2 and the percent error is 4.000%.
The division is the entire point. An error of 2 means very different things depending on what you were measuring: 2 grams out of 50 is a sloppy result, 2 grams out of 50,000 is excellent. Dividing by the true value strips out the scale and leaves something comparable across experiments, instruments and units.
Note which value sits on the bottom. It is the true or accepted value, never your measurement — that is what makes the result a statement about your error rather than about your equipment's opinion of itself. Dividing by the experimental value produces a different number, and it is a common enough slip that it is worth checking in any formula you are handed.
Percent error is conventionally reported unsigned because the question is usually "how far off was I", not "in which direction". Two labs at +3% and −3% are equally accurate and the sign would obscure that.
But the sign carries real diagnostic information, which is why this page shows the raw error separately. Random error scatters either side of the true value; systematic error lands consistently on one side. A dozen trials all reading low is not bad luck — it is a mis-calibrated instrument, a consistent parallax, an uncorrected buoyancy effect. If every run has the same sign, stop repeating the measurement and go and find the bias.
There is no universal threshold — acceptable error is set by the field and the method, not by the arithmetic. In an introductory teaching lab, under 5% is usually a good result and under 10% acceptable. A gravimetric analysis in an analytical chemistry lab would be expected under 1%. Some biological and field measurements tolerate 20% or more, because the underlying variation is genuinely that large. Always check the tolerance for the method rather than assuming a number is fine because it looks small.
One case has no answer at all: when the true value is zero, percent error is undefined, because you would be dividing by zero. This is not a quirk of the formula but a real limitation — "how far off, proportionally, from nothing" has no meaning. The calculator flags it rather than returning something misleading. Where the accepted value is legitimately zero, report the absolute error with its units and say so explicitly.
Working with several trials rather than one? The standard deviation calculator quantifies the scatter, which is the other half of the picture — accuracy and precision are separate properties and a result can have one without the other.
Percent error measures how far an experimental or measured value is from a known, accepted true value, expressed as a percentage: |experimental − true| / |true| × 100. It's the standard way labs and classrooms report how accurate a measurement was against a known reference.
Percent error is meant to report the size of the miss, not its direction — the absolute value strips the sign so a measurement that came in high and one that came in low by the same amount get the same percent error. This calculator also reports the signed absolute error (experimental − true) separately, so the direction isn't lost — just kept out of the percentage itself.
There's no single universal cutoff — it depends entirely on the field, the instrument, and what's being measured. A physics lab timing a pendulum with good equipment might target under 1–2%, while some biology or chemistry experiments with more natural variability routinely accept 10% or higher as reasonable. Compare your result against what's typical for your specific experiment rather than assuming a fixed threshold applies everywhere.
No, and mixing them up is a common mistake. Percent error compares a measured value against a known, accepted true value — that's what this calculator computes. Percent difference compares two experimental values to each other when neither one is a trusted reference, typically as the absolute difference divided by the average of the two values, times 100. Use percent error whenever you have a correct answer to check against; reach for percent difference only when comparing two measurements with no accepted "true" value between them.
Worked example: a measured value of 48 against a true value of 50: absolute error = 48 − 50 = −2, and percent error = |48 − 50| / |50| × 100 = 2/50 × 100 = 4%. The negative absolute error shows the measurement came in low; the percent error strips that sign to report the size of the miss.